Chemical Engineering and Processing 70 (2013) 294 300

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Chemical Engineering and Processing:Process Intensication

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Short communication

The shr c d

Dominik l c

a Interdisciplinb Leibniz Instituc Faculty of Agr erma

a r t i c

Article history:Received 7 JanReceived in reAccepted 3 MaAvailable onlin

Keywords:Shrinking coreMass transporAnaerobic digeLignocellulosicHydrothermal

aerobt equantro

of mcuba

creasm3 (0atile

1. Introdu

The shortage of resources is a challenge for the energy produc-tion. It will be necessary to use renewable energy sources. Theenergetic utilization of organic residues is an interesting possi-bility, because they are left over in high amounts in agriculture.The residuecomposite oa phenolic mframeworkinuence frutilization o

Comparetion kineticpump and sand Panwarfrom lignoc

BatstoneNo. 1 (ADMprocess. In limiting stedrates. Theyfor both promodel if neVavilin et al

CorresponE-mail add

ysis oin two phases. The First one is the colonization of the particle sur-face by hydrolytic bacteria. In a second phase the bacteria grow onthe surface and the particle shrinks.

In the case of lignocellulosic bers the shape of the particles isnot spherical but rather cylindrical, as suggested by [10]. He also

0255-2701/$ http://dx.doi.os mostly consist of lignocellulosic bers. These are af carbohydrates (cellulose, hemicelluloses) and lignin,acromolecule. The lignocelluloses provide the plants

. It also protects the plant against physical and biologicalom the environment. These properties deteriorate thef residues for energy production, [1].d to energy crops the methane yield and the degrada-

of lignocelluloses are lower. The bers also impede thetirring properties of the ferment, Chen et al. [2], Karla

[3,4]. Pretreatments similar to the ethanol productionellulosic matter could solve these problems, [57].

et al. [8] published the Anaerobic Digestion Model1) and gave a good standard for modeling the biogascase of straw and other crops rich of ber the ratep is the disintegration and hydrolysis of the carbohy-

assumed in a rst approximation a rst order kineticcesses and suggested a more accurate surface relatedcessary. This surface related model was developed by. [9]. They assumed shrinking spherical particles for the

ding author. Tel.: +49 381 498 3340; fax: +49 381 498 3346.ress: dominik.da.rocha@gmail.com (D. da Rocha).

mentioned that the macroscopic shape of the particles was not asimportant for the hydrolysis kinetics, because in the scale of theorganisms the particles shape appears nearly planar. However, themicrostructure of the plant material consists mostly of lignin, cel-luloses and hemicelluloses and these are organized in a structureof cylindrical bundles.

Furthermore the particles do not shrink because the frame-work of the lignin is not biodegradable. Therefore, in this paperthe shrinking core model was used to describe the hydrolysis oflignocellulosic framework.

2. Materials and methods

2.1. Materials

Wheat straw was used to study the biological degradation oflignocellulosic bers. To get bers with nearly same size, the strawwas comminuted in a knife mill and it was sieved through 1 mmand 0.25 mm mesh. For investigations the sieve residual of the0.25 mm mesh was used. The water content of the straw amountedto 8.7 wt%. It was dried at 105 C for 17.5 h. The dry matter wascombusted at 600 C for 8 h and yielded an ash content of 3.0 wt%of the dry matter.

see front matter 2013 Elsevier B.V. All rights reserved.rg/10.1016/j.cep.2013.05.003inking core model applied on anaerobi

da Rochaa,, Eckhard Paetzoldb, Norbert Kanswohary Faculty, University of Rostock, Germanyte for Catalysis, Rostock, Germanyicultural and Environmental Sciences, Agricultural Technology, University of Rostock, G

l e i n f o

uary 2011vised form 23 January 2013y 2013e 6 June 2013

modeltstion

bers treatment

a b s t r a c t

In this study, the gas formation of anmodel is based on the mass transportreated wheat straw. Additionally a co

With untreated straw the beginningsurrounding uid lm. With further inlayer limited the degradation.

A short hydrothermal treatment deThe gas yield of the straw was 0.54 d

in 0.51 dm3 (0 C, 1 atm) per gram volcarbon dioxide (51 vol%).

ction hydrolm/locate /cep

igestion

ny

ic digestion was analyzed by the shrinking core model. Thistions. The experiments were carried out with hydrothermal

l group of untreated wheat straw was examined.icrobiological growth was limited by convection through thetion time the bacteria formed a biolm. Diffusion through this

ed the convection-limited phase.C, 1 atm) per gram volatile solid. The pretreated straw yieldedsolids with the same mean content of methane (49 vol%) and

2013 Elsevier B.V. All rights reserved.

f cellulose and sewage sludge. They divided the kinetic

D. da Rocha et al. / Chemical Engineering and Processing 70 (2013) 294 300 295

Nomenclature

Symbolsa b B Bo c D Da g G k

m n r R t V X Y

Indices0 1st B C CH4CO2eff end ex F G P R S

The ino(Dummerstmanure. Wato 91.9 wt%After takingat 20 C to dies were caof 400.

2.2. Anaero

The gas fYield Test,digesters. TThe whole 600) at 38the producThe digestestraw. Threown gas forstoichiometric coefcient hydrogenstoichiometric coefcient oxygenbacteriaBodenstein numberconcentrationdiffusion coefcientDamkhler numberstoichiometric coefcient of gasgasreaction rate constant, convective transfer coef-cientmassstoichiometric coefcient carbonvariable radiusconstant radiustimevolumeconversion of substrateyieldrelative time (time over incubation time)

relative radius (core radius over ber radius)incubation timeconcentration ratio of bacteria in uid per bacteriain the solid

at starting timerst order kineticbacteriacore, convectivemethanecarbon dioxideeffectiveat end of incubation timeexchangeuidgasparticlereactionsubstrate, solid

culum arose from an agricultural anaerobic digesterorf, Germany), mainly fed with corn silage and cowter and ash contents were determined. They amounted

of water and 20.8 wt% ash referring to the dry matter. from the digester, the inoculum was stored two weeksecrease own gas formation. The light microscopic stud-rried out with a Carl Zeiss Laboval 4 at a magnication

bic digestion

ormation was observed according to the Hohenheimer [11]. Therefore 100 ml glass syringes were used ashey are sorted in a carousel for mixing the ferment.apparatus was placed in an incubator (Memmert INE-C. The syringes had a scale of 1 ml steps to measureed gas. They were sealed with highly viscous parafn.r was lled with 30 g of inoculum and 1 g of wet wheate syringes were just lled with inoculum to subtract itsmation from the inoculum.

Fig. 1. Wheattimes with a lthe incubation

The carba Brel & Knected to adeterminatinto the asitor. When was reachethis assembdeterminedwas calcula

2.3. Hydrot

The hyd(Parr reactowas equipprunning at deionized w40 min. By stopped bycooling to observed b

2.4. Charac

The gas per gram dsolids. The and 49 vol%

The stranearly the or 0.51 dm3

bon dioxideamounted t

The degmicroscopedays of incuover the tim straw before (a) and after (b) 40 days of incubation, magnied 400ight microscope. The microstructure of the straw is preserved after.

on dioxide and methane contents were measured withjr gas monitor type 1302. This device was tightly con-

500 ml Erlenmeyer ask by the gas inlet and outlet. Forion of the gas, 2 ml of the formatted biogas were injectedk and well mixed by the internal pump of the gas mon-the maximum capacity of the gas monitor (4000 ppm)d, the ask was ushed with silica gel dried air. Withly the ratio of carbon dioxide and methane could be

with a precision of 2%. The mass of the produced gasted under assumption of ideal gas behavior.

hermal treatment

rothermal treatment was done in a 100 ml autoclave

r No. 4593, temperature controller 4842). The reactored with a magnetically coupled blade stirrer, which was1000 rpm. It was lled with 6 g straw (wet) and 54 gater. The heat up time to reach 200 C amounted to

reaching the predened temperature the reaction was cooling the reactor in an ice-water bath. The time for40 C required less than 5 min. The pressure could bey a gauge (050 bar).

terization

yield of the untreated straw amounted to 0.70 g of gasry matter or 0.54 dm3 (0 C, 1 atm) per gram volatilemean chemical composition of the gas was 51 vol% CO2

CH4.w, which was treated at 200 C for a short time, hassame biogas yield, 0.67 g of gas per gram dry matter(0 C, 1 atm) per gram volatile solids. The mean car-

content was 49 vol% and the mean methane contento 51 vol%.radation of straw bers was examined under a light. Fig. 1a and b shows the straw bers before and after 40bation. The micro structure of the bers is unscathede.

296 D. da Rocha et al. / Chemical Engineering and Processing 70 (2013) 294 300

Fig. 2. Schemeshows the shr

3. The shri

3.1. Model

The shrinwell explainand uids. cle and reaproducts caunreacted s

The mas

- Convectiosurroundi

- Diffusion - Reaction a- Diffusion - Convectio

uid main

Primarilof particles.uid-partic

Subramaing core maddition, thPET (polyet

Fowler alimited thetigation thesulfur-consyield and a

In the cathe particleas a functioover ber ra

X = 1 2

If the cothen the rel

= X

If diffusi

= X + (1

If the rea

= 1 (1

3.2. The reaction mechanism

The reaction mechanism for anaerobic digestion is very com-plex. Sahm divided the degradation in a chain reaction systemof four phases. The degradation starts with the hydrolytic andacidogenic

degrfolloacid,nogeke eon. Id ou

reac of cee conreforationestibon dion [2

b +(

+(

forme the

e con

conv

S,0 mS,0

his eqIf a c

CO2

mas of b

mCO2

hat t

mCO

bactvers

CO2,e of mass ux steps in the shrinking core model. The section of a berinking unreacted core over the time, Levenspiel [14].

nking core model

basics

king core model was rst published by [12,13], and wased by [14]. It describes the mass ux between particlesThe basic idea is that the uid ushes into the parti-cts to uid and solid products respectively. The uidn leave the particle, while the solids form a layer. Anhrunken core remains in the middle of the particle.s ux proceeds in ve steps (Fig. 2):

n of reactants from the uid main body through theng uid lm.through the solid products layer.t the cores surface.of uid products through the solid layer.n of uid products through the uid lm back in the

body.

y the model was developed to describe the combustion In the course of time it has been applied to many otherle-reactions.nian et al. [25] published the application of the shrink-

odel on the discharge of metal hydride electrodes. Ine shrinking core model could describe the hydrolysis ofhylene terephthalate) in sulfuric and nitric acid, [15,16].nd Crundwell [17] showed that a formed sulfur layer

leaching of zinc sulde by ferric sulfate. In this inves- formation of the sulfur layer was prevented by addinguming bacteria (Thiobacillus ferrooxidans). A higherfaster leaching were the results.se of the anaerobic digestion of lignocellulosic bers,s shape is a cylinder. According to [14] the conversionn of the shrinking core radius is: ( = rc/R, core radiusdius):

(1)

drates phase acetic metha

Noidigestipointeoveralldationthe rat

Thedegradto: Digto carbequati

CnHaO

Thebecaus

3.3. Th

The

X = m

In tstraw.

mS = mThe

growth

mB = (So t

mS = (The

the con

X = mnvection through the surrounding uid lm controlsative reaction time as function of the conversion is:

(2)

on through the solid layer controls:

X) ln(1 X) (3)

ction rate controls the mass ux:

X)1/2 (4)

3.4. Reactio

3.4.1. FluidAccordin

dnBSexdt

= kC (

The masbe assumedface is negl

Sex = 2LR phase. Macromolecules like proteins, fats and carbohy-ade to higher organic acids and alcohols. The acetogenicws. Higher organic acids and alcohols are reduced to

carbon dioxide and hydrogen. The last phase is thenic, where methane is formed, [18].t al. determined the rate-limiting step of anaerobicn experiments with glucose, starch and cellulose, theyt, that the degradation of cellulose characterizes thetion rate. The maximum rate constant for the degra-llulose was 1.25 per day and for the methanogenesisstant amounted to 10.9 per day, Noike et al. [19].e the rate of the biogas formation is nearly equal to the

rate of the straw bers. The reaction system is assumedle carbohydrates (CnHmOk) react in presence of bacteriaoxide and methane. According to the simplied Buswell0]:

n a4

b2

)H2O

(n

2 a

8+ b

4

)CO2

n

2+ a

8 b

4

)CH4 (5)

ation of ammonia and hydrogen sulde is neglected straw consists mainly of carbohydrates.

version

ersion is calculated by:

mS (6)

uation mS,0 is the mass of fermentable substance in theomplete conversion is assumed, it is given by:

+ mCH4 + mB (7)s of formed carbon dioxide and methane depends onacteria:

+ mCH4)YB (8)he mass of substrate is:

+ mCH4)(1 + YB) (9)eria yield (YB) could be canceled from the equation ofion:

nd + mCH4,end (mCO2 + mCH4)mCO2,end + mCH4,end

(10)

n kinetics

lm controlsg to [14] the mass ux equation for convection is:

cB,F cB) (11)

s exchange surface is the bers lateral surface. It could that the ber is much longer than thick. Hence the endigible.

(12)

D. da Rocha et al. / Chemical Engineering and Processing 70 (2013) 294 300 297

Additionally the concentration at the ber surface is muchsmaller than in the uid, while convection is controlling the massux.

cB,F cB c

The bactby the biocB,SdV = cB,dnB = cB,S

All inser

cB,02LrC2LRdt

The equber radius

drCdt

R= k

A dimenreduced to aof bacteria

= rcR

= t

DaC =kC

R

= cB,FcB,S

If the conmass ux, t

d

d= DaC

3.4.2. ReactThe mas

dation is:

dnBSexdt

= kRc

Now the

Sex = 2LrCIf the rea

small or thcore is near

cB cB,FThe chan

cB,S2LrC2LrCdt

Multiplithe equatio

drCdt

R= k

A dimensionless equation follows. The parameters could bereduced to a 1st order Damkhler number and a concentration ratioof bacteria in uid per bacteria in the solid [26].

kR

R

DaR

Diffus law

= Def

exch

Lr

contion a

rCR

ln(

udin

LrCLdt

ltipliuatio

=rC

Deff

R2

imed toia in

eff

R2

Bo

ln(

Combot a s

of r

= d

reforipro

ln(

integhm iince le scB,F (13)

eria amount is the cell density in the solid multipliedlm volume. The biolm volume is tube shaped.dnB =Sd(L(R2 r2C )) = cB,S2LrCdrC2LrCdrC (14)

ted in the mass ux equation:

drC = kCcB,F

ation multiplied by incubation time and divided by the:

C

R

cB,FcB,S

R

rC

sionless equation follows. The parameters could be 1st order Damkhler number and a concentration ratio

in uid per bacteria in the solid [26].

(15)

(16)

(17)

(18)

vection through the surrounding uid lm controls thehe change of the relative radius by time is:

(19)

ion rate controlss ux equation if the reaction rate controls the degra-

B (20)

exchange surface is the cores surface:

(21)

ction rate controls the degradation, the biolm will bee diffusion is so fast the bacteria concentration at thely the uid concentration.

(22)

ge of the core radius is described as:

drC = kRcB

ed by incubation time and divided by the ber radiusn is:

R

R

cB,FcB,S

DaR =

d

d=

3.4.3. Fick

dnBSexdt

The

Sex = 2The

centra

dnB2Ldt

dnB2Ldt

Incl

cB,S22

Muthe eq

drCdt

R

d

d=

A dreducebacter

Bo = D

d

d=

3.4.4. If n

change

dtotal

Thethe rec

d

d=

To algoritand Prexamp(23)

(24)

sion controls gives the mass ux for diffusion:

fdcBdr

(25)

ange surface is the variable core surface:

(26)

centration at the core will always be zero and the con-t the bers surface is equal to the uid concentration:

dr

r= Deff

0cB,F

dcB

rCR

)= DeffcB,F

g Eq. (10):

drC ln(

rCR

)= DeffcB,F

ed by incubation time and divided by the ber radiusn is:

Deffln(rC/R)

R

cB,FcB,S

cB,FcB,S

R

rC ln(rC/R)

nsionless equation follows. The parameters can be the Bodenstein number and a concentration ratio ofuid per bacteria in the solid [26]

(27)

)(28)

ining mass transport mechanismsingle transport mechanism controls the mass ux, theelative radius can be added.

Conv + dDiff + dReace, the developed equations can be combined by addingcal:

)/Bo /DaC 1/DaR(29)

rate the ordinary differential equation a RungaKottancluded in the software MATLAB was used, Dormand[21]. The differential equation is solved in a MATLABript in the appendix.

298 D. da Rocha et al. / Chemical Engineering and Processing 70 (2013) 294 300

4. Results and discussion

4.1. Applicability of the shrinking core model

For the eand the beto measureCounting thof active orgparticles. Thparticles we

That is was assufactor in twith the saing core mdifferent inerence. Thindirectly.

The redutage that thinstrument

To descr(Eq. (1)). Tare longer in two spawas also o[22].

The degrregions. Heexposed gluin the radialases can dproceeds inis soluble in(R) in the eticles. The Rstraw-micrber only hthe ferment

The degconvection-cellulose bument was tothe straw.

4.2. Biogasf

The micrally this delIn this phasubstrate [2

The gas fThe reactionCompared tdiffusion lim(Fig. 3a).

The equLAG-phase it seems thIf the surfafor diffusiotion with the bacter(Fig. 4a).

a and b) Gas formation of the untreated (a) and pretreated straw (b), therve was calculated with the shrinking core model (diffusion controlled,

with Bo = 0.25 and = 1 for (a) and (b)). It tted the course of the mea-ints more accurate compared to a 1st order Kinetic (k1st = 0.1 s1 for (a) and2 s1).

ogasformation of the pretreated straw

pretreatment of the straw increases the degradation ating of the biogas formation. The hemicellulose of the strawtracted by the hydrothermal treatment. It was more avail-r the bacteria. The smaller gas yield of the treated straw

indicator for the formation of indigestible reaction products the hydrothermal treatment (Fig. 3b).rder to reduce this effect the heat up time for the hydro-l treatment will have to be reduced. A more complextus will be necessary. For example a Percolator with pre-

water can reduce the heat up time, according to [24]. for the pretreated straw the gas formation course was ttedt order kinetic. The rate constant (k1st) amounted to 0.12 s1.rinking core model with a duffusion limited rate equation isccurate compared to the 1st order kinetic (Fig. 4b).

plementation in the ADM1

ADM1 and other anaerobic digestion models were usuallyon insteady mass balance. The kinetic equations were solvedderivation of the concentration by time. So the diffusion

rate Eq. (28) was formed to such an expression. conversion was dened as:

cscS,0quation suggested by [14], the bacteria concentrationr radius had to be known. These parameters were hard. The different species of bacteria were not dened.e cells under the microscope did not give the numberanisms. There were also microorganisms on and in theey were not countable under a microscope because there opaque.why the parameter for the bacteria concentrationmed to a value of 1. This parameter is a constanthe Eqs. (19), (24), (28), (29) so that experimentsme inoculum were comparable. Maybe the shrink-odel could be used to compare experiments withoculums, if a standard substrate is used as ref-e parameter of the bacteria could be calculated

ction to dimensionless parameters had the disadvan-e absolute value got lost. However, it was a helpful

to compare the degradation kinetics.ibe the geometry of the ber a cylinder was assumedhis relationship is valid for any other bodies thatthen thick. The equation described the degradationtial dimensions. This two-dimensional degradationbserved in the enzymatic degradation of cellulose

adation of the cellulose ber started in the amorphousre the endoglucanases broke the -glycosidic bonds. Itcose molecules from the chain. This is the degradationl direction (rst spatial dimension). The cellobiohydro-egrade the ber to cellobiose units. This degradation

axial direction (second spatial dimension). Cellobiose water and can leave the ber. Therefore the ber radiusquations is not equal to the geometric size of the par-adius is rather the size of the cellulose bundles in the

o-structure. So hollow spaces and swelling of the strawave an effect on the untreated straw at the beginning ofation.radation of the untreated straw started with alimiting step. In this step the bacteria had to reach thendles. The main effect of the hydrothermal pretreat-

expose the bundles by solving the hemicelluloses from

ormation of the untreated straw

oorganisms started the degradation with a delay. Usu-ay is interpreted as the LAG-phase of bacterial growth.se the microorganisms adapt their metabolism to the3].ormation course was calculate with a 1st order kinetic.

rate constant (k1st) for the untreated straw was 0.1 s1.o a 1st order kinetic the shrinking core model with aited rate (with Bo = 0.25 and = 1) is more accurate

ation for convection limited mass ux tted thewell with a Damkhler number of 0.6. Thereforeat the microorganisms had to settle on the ber.ce of the ber is completely covered, the equationn-limited degradation tted the measured degrada-a Bodenstein number of 0.263. The parameter foria concentration was assumed to value of 1

Fig. 3. (solid cuEq. (28)sured pok1st = 0.1

4.3. Bi

Thebeginnwas exable fowas anduring

In othermaapparaheated

Alsoby a 1sThe shmore a

4.4. Im

Thebased to the limited

The

X = 1

D. da Rocha et al. / Chemical Engineering and Processing 70 (2013) 294 300 299

Fig. 4. (a and bconvection limphase the coustraw (b) degr

X = 1 (

rCR

Therefor

rCR

=(

cscS,0

Ficks lawder:

dnB2Ldt

ln(

The chanstrate. So tlogarithm wby the ferm

dcSdt

= 4VR ln

Accordinbacteria conduce their eout. Therefoconcentratilength, diffThese param

the dimension mole per time and volume. The following expressioncould implemented to the ADM1.

dcS kHyd

ln( ) (30)

pracase

t kinece t

andther

rmenctan

clus

anad outfusio

the bic Dreactncrees arhe abenta

wled

nks tdt=

Thetwo phdefaulresidenkinetic

Anobed fethe rea

5. Con

Thepointethe diftion ofAnaeroof the ment ipentoshand tunferm

Ackno

Tha) Shrinking-core-plot of the untreated (a) straw, at the beginning theited Eq. (19) tted the course of the measured points. After this initialrse was calculated for the diffusion limited Eq. (28). The pretreatedades according to the diffusion limited kinetic.

)2

e the relative radius was:)1/2

of diffusion in the partially integrated form for a cylin-

rCR

)= DeffcB,F

ge of bacteria was proportional to the change of sub-he biomass yield was inserted. The exponent in theas extracted to a factor and the equation was dividedenter volume (VR).

LDeffcB,F(cs

cS,0

)

g to [22] the hydrolysis rate did not depend on thecentration. Because the microorganisms began to pro-xoenzymes if other easier carbon sources were runningre the change of substrate was independent from theon of the bacteria in the uid. Furthermore are berusion coefcient and fermenter volume are constants.

eters were combined to a single constant (kHyd) with

References

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[2] Y. Chen, Jreview, B

[3] M.S. KarlWaste 17

[4] Sharma, biomass

[5] I. Ballestwheat s496508

[6] O. Bobletpolysacchdiversity2005, pp.

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ime will be modeled, the difference between 1st order the shrinking core model will be recognizable.

possible application is the modeling of batch or solidters if it is necessary to calculate the concentration ofts over the residence time.

ions

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gment

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The shrinking core model applied on anaerobic digestion1 Introduction2 Materials and methods2.1 Materials2.2 Anaerobic digestion2.3 Hydrothermal treatment2.4 Characterization

3 The shrinking core model3.1 Model basics3.2 The reaction mechanism3.3 The conversion3.4 Reaction kinetics3.4.1 Fluid film controls3.4.2 Reaction rate controls3.4.3 Diffusion controls3.4.4 Combining mass transport mechanisms

4 Results and discussion4.1 Applicability of the shrinking core model4.2 Biogasformation of the untreated straw4.3 Biogasformation of the pretreated straw4.4 Implementation in the ADM1

5 ConclusionsAcknowledgmentReferences